Remark 2 Linear convergence has been achieved in [1]}, [2]}, [3]} for only unbiased \(\delta \) -contracted compressors. Though the time-varying uniform quantizers in [4]}, [5]}, [6]} are biased, it is unclear whether their algorithms can adapt to other compressors and how the network and compression affect the convergence rates. To the best of our knowledge, COLD is the first distributed algorithm with linear convergence rate for biased \(\delta \) -contracted compressors.

